A time-variant filtering approach for non-stationary random signals based on the fractional convolution

Image Processing Operators Based on the Gyrator Transform: Generalized Shift, Convolution and Correlation

“…Shift operation has also been used in optical systems; for instance, shift operation is utilized at the input plane of the joint transform correlator (JTC) architecture in order to place two non-overlapping data distributions side-by-side [7,8]. The usual shift, convolution and correlation operators have been defined using the fractional Fourier transform [9,10] and these fractional operators were applied to the sampling theorem for fractional bandlimited signal [11], time-variant filtering for non-stationary random signals [12] and prediction, interpolation and filtering of α-stationary random signals [13], where α is the fractional order of the fractional Fourier transform [10].…”